To factor the expression \( 8w + 16 \) using the greatest common factor (GCF), we first need to determine the GCF of the coefficients 8 and 16.
The GCF of 8 and 16 is 8.
Now, we can factor 8 out of the expression:
\[ 8w + 16 = 8(w + 2) \]
Therefore, if we look at the options provided:
- A: \( 2(4w + 8) \)
- B: \( 6(2w + 10) \)
- C: \( 4(2w + 4) \)
- D: \( 8(2w + 2) \)
The correct factorization that uses the GCF and matches our expression \( 8(w + 2) \) is:
D: \( 8(2w + 2) \)
So the choice is D.